Shells, orbit bifurcations and symmetry restorations in Fermi systems

TL;DR

This paper develops a semiclassical periodic-orbit theory to analyze nuclear shell structures, bifurcations, and symmetry breaking phenomena in Fermi systems, explaining complex nuclear shapes and shell effects with good quantum-classical agreement.

Contribution

It introduces an improved stationary-phase method within phase-space path integrals to study bifurcations and symmetry breaking in nuclear potentials, linking classical orbits to quantum shell effects.

Findings

Explains the origin of the double-humped fission barrier.

Describes the semiclassical basis for shape asymmetries and tetrahedral configurations.

Shows good agreement between semiclassical and quantum shell structures.

Abstract

The periodic-orbit theory based on the improved stationary-phase method within the phase-space path integral approach is presented for the semiclassical description of the nuclear shell structure, concerning the main topics of the fruitful activity of V. G. Solovjov. We apply this theory to study bifurcations and symmetry breaking phenomena in a radial power-law potential which is close to the realistic Woods-Saxon one up to about the Fermi energy. Using the realistic parametrization of nuclear shapes we explain the origin of the double-humped fission barrier and the asymmetry in the fission isomer shapes by the bifurcations of periodic orbits. The semiclassical origin of the oblate-prolate shape asymmetry and tetrahedral shapes is also suggested within the improved periodic-orbit approach. The enhancement of shell structures at some surface diffuseness and deformation parameters of such shapes are explained by existence of the simple local bifurcations and new non-local bridge-orbit bifurcations in integrable and partially integrable Fermi systems. We obtained good agreement between the semiclassical and quantum shell-structure components of the level density and energy for several surface diffuseness and deformation parameters of the potentials, including their symmetry breaking and bifurcation values.